On the Causality of Mixed-Signal and Hybrid Models

  • Jie Liu
  • Edward A. Lee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2623)


This paper extends the application of the Cantor metric as a mathematical tool for defining causalities from pure discrete models to mixed-signal and hybrid models. Using the Cantor metric, which maps timed signals, continuous or discrete, into a metric space, we define causality as contractive properties of processes operating on these signals. Thus, the Banach fixed point theorem can be applies to establish conditions for the existence, uniqueness, and liveness of the behaviors for mixed-signal and hybrid systems. The results also provide theoretical foundations for the simulation technologies for such systems, including the time-marching strategy, evaluation of feedback loops, and the necessity of supporting rollback.


Functional Process Hybrid Automaton Denotational Semantic Local Lipschitz Condition Continuous State Variable 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jie Liu
    • 1
  • Edward A. Lee
    • 2
  1. 1.Palo Alto Research CenterPalo Alto
  2. 2.Department of EECSUniversity of CaliforniaBerkeley

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